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Republication of: The mechanics of matter particles in general relativity. Translation from [Z. Phys. 67, 826–844 (1931)]. (English) Zbl 1188.83017
Summary: “The solution of the equations of gravitation for an arbitrarily moving charged particle is given in first approximation. The equations of motion show up as conditions for the existence of solutions. On this example, the following problems are formulated: 1. of the uniqueness of the potentials; 2. of constancy of charge and mass of the particle; 3. of the conditions at infinity. The linearisation of the equations on a Euclidean background is discussed. The mathematical means necessary for the computational treatment of the problem are developed.”
An editorial note to this paper can be found in this issue preceding this Golden Oldie [Gen. Relativ. Gravitation 42, No. 4, 985–987 (2010; Zbl 1188.83006)]. The companion paper to this one can be found in this issue after this Golden Oldie [Gen. Relativ. Gravitation 42, No. 4, 1011–1048 (2010; Zbl 1188.83018)].
Original paper: M. Mathisson [“Die Mechanik des Materieteilchens in der allgemeinen Relativit√§tstheorie”, Z. Phys. 67, 826–844 (1931; Zbl 0001.24602)]. Reprinted with the kind permission of the Editors of European Physical Journal D, the current owner of the publication rights. Translated by Anita Ehlers.

83C10 Equations of motion in general relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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